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Dr. Sinn, PSYC 301 2 Way ANOVA

Factorial Design Two Way ANOVAs

2 Independent Variables Examples

IV#1 IV#2 DV

Drug Level Age of Patient Anxiety Level

Type of Therapy Length of Therapy Anxiety Level Type of Exercise Type of Diet Weight Change

Toy Color Gender Satisf. with Toy

Key Advantages

Compare relative influences on DV Examine interactions between IV

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Example Two Way ANOVAs

Toy Study

IV: Toy Color (Blue, Pink)

IV: Gender (Boy, Girl)

DV: Satisfaction with Toy

Terms

Factors: __ * ___ * ___

Levels (a,b)

Design: ___ x ___ Main Effect, collapsing

Interaction

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Main Effects Two Way ANOVAs

Main Effect forToy Color?

Compare Column

Means

Toy ColorBlue

(1)

Pink

(2)

Sex

Boy(1)

7

6

5

2

3

4

Girl

(2)

4

56

12

1011

M=5.5 M=7.0

M=8.0

M=4.5 Main Effect for

Gender?

Compare RowMeans

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Interactions- Cell Means Two Way ANOVAs

Toy Color

Blue (1) Pink (2)

Sex

Boy (1)

7

6

5

2

3

4

Girl (2)

4

56

12

1011

M=6 M=3

M=5 M=11

Graph cell

means to

examine

possibility of

interaction

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Interactions-Graph Two Way ANOVAs

General rule of life: If two lines cross, it probably means something.

0

2

4

6

8

10

12

Blue Toy Pink Toy

Boy

Girl

Non-parallel lines suggests interaction.

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SPSS: Data Input #1 Two Way ANOVAs

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SPSS: Data Input #2 Two Way ANOVAs

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SPSS: Analysis, Step #1 Two Way ANOVAs

Go to Analyze, General Linear Model, Univariate

Move DV to Dependent Variable

Move 2 IVs to Fixed Faxtors

Step #1

Step #2

Step #3

Step #4

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Select Plots; Graph sample means with two IVs

If one IV has more levels, put on Horizontal Axis

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Select Options

Ask for Descriptive Statistics

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Select Post Hoc

Do Post Hoc (SNK) for IVs with 3+ levels

Not required in this example; both IVs have only 2 levels:color (blue & pink), sex (boy & girl)

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SPSS Output #1 Two Way ANOVAs

Descriptive Statistics

Dependent Variable: satisf

6.00 1.000 3

5.00 1.000 35.50 1.049 6

3.00 1.000 3

11.00 1.000 3

7.00 4.472 6

4.50 1.871 6

8.00 3.406 6

6.25 3.194 12

sex

boy

girlTotal

boy

girl

Total

boy

girl

Total

color

blue

pink

Total

Mean Std. Deviation N

etw ee n-Subje cts Factors

blue 6

pink 6

boy 6

girl 6

1

2

color

1

2

sex

ValueLabel N

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Tes ts of Betw een-Subjects Effects

Dependent Variable: s atis f

104.250a 3 34.750 34.750 .000468.750 1 468.750 468.750 .000

6.750 1 6.750 6.750 .032

36.750 1 36.750 36.750 .000

60.750 1 60.750 60.750 .000

8.000 8 1.000581.000 12

112.250 11

Source

Corrected ModelIntercept

color

sex

color * sex

ErrorTotal

Corrected Total

Type III Sum

of Squares df Mean Square F Sig.

R Squared = .929 (Adjusted R Squared = .902)a.

SPSS Output #2: Two Way ANOVAs

BG

WG

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SPSS Output #3: Two Way ANOVAs

blue pink

color

2

4

6

8

10

12

EstimatedMarginalMeans

sex

boy

girl

Estimated Marginal Means of satisf

Note: post-hoctests are needed

only when you

have 3+ levels of

an IV (here we

dont).

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Write-up Two Way ANOVAs

The hypotheses were supported. [1] There was a

main effect fortoy color. Pink toys (M=7.00)

elicited significantly more satisfaction than blue toys

(M=5.5), F(1,8) = 6.750, p .05. [2]There was also

a main effect forsex. Girls were significantly more

satisfied (M=8.00) than boys (M=4.50),

F(1,8)=36.750, p .05.

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Write-up (cont.)Two Way ANOVAs

[3] Additionally, there was a significant interactionbetween color and sex, F(1,8) = 60.75, p.05.

Boys and girls appear equally satisfied with blue

toys. Switching to pink toys, however, raised

satisfaction for girls but decreased satisfaction for

boys. Sex accounted for only a small amount of

variance in satisfaction (2= .0601), but color (2

=

.3274) and the interaction (2= .5412) accounted

for a large amount of variance.

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Two-Way ANOVA Cont.

Announcements

Review Study Guide for Final

Homework: Influence Study

Homework: Teamwork & Feedback Study, write-ups

Explain Purpose of 2nd ANOVA Lab

Studying for Final Computational Review for Final

ReviewName That Stat Exercises

Practice SPSS on computer

Review Old Computations

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Source of Variation Table for 2-way ANOVA

Three possible influences on DV -- factors

A: IV #1

B: IV #2

C: Interaction

Sum of Squares (SS) always given

Calculating Degrees of Freedom by hand

dfA = a-1

dfB = b-1

dfA*B = (a-1)*(b-1) dfwg = a * b * (n-1)

dfTotal = N1

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Table Reading Keys

1. Three Fs use same formula MSBG / MSWG = MSSpecific Factor/ MSError For example: MSA / MSError

2. Factor significant if p .05

3. MS = SS/df for each factor and error

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Tes ts of Betw een-Subjects Effects

Dependent Variable: s atis f

104.250a 3 34.750 34.750 .000468.750 1 468.750 468.750 .000

6.750 1 6.750 6.750 .032

36.750 1 36.750 36.750 .000

60.750 1 60.750 60.750 .000

8.000 8 1.000581.000 12

112.250 11

Source

Corrected ModelIntercept

color

sex

color * sex

ErrorTotal

Corrected Total

Type III Sum

of Squares df Mean Square F Sig.

R Squared = .929 (Adjusted R Squared = .902)a.

Source of Variation Table from Toy Study

BG

WG

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Age &

Intelligence(2-way ANOVA)

Task

Fluid Crystalized

Age

65 105100

95

100

10095

110

100

75 85

90

95

85

105

95

100

105

85 85

80

75

80

105

95

100

100

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Important Means

Main effect for Task? Main effect for Age?

Graph it

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Calculate degrees of freedom by hand:

dfA

dfB

dfA*B

dfError

dfTotal

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Complete Table with these SS

SSTask= 759.375 SSAge = 452.083

SSTask*Age = 356.250

SSError

= 406.250

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SPSS Data Entry

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Check Output

What means pertain to Effect of Task Effect of Age

Effect of interaction

Is there a . Main effect for Task Main effect for Age

Interaction

Is Post Hoc Required? Explain graph

Do complete Write-up

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2-way ANOVA: Age & Intelligence

First, Id like tothank my statistics

teacher for

devising such a

creative, exciting,

and enriching

exercise. My life

will neverbe thesame.

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2-way ANOVA: Age & Intelligence

The hypotheses were supported.

Participants scored significantly lower on tasks usingfluid (M=89.58) rather than crystallized intelligence

(M=100.83), F(1,18) = 33.46, p

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Interpreting 2-way Outcomes

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Interpreting 2-way Outcomes (cont.)

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Bogus Winthrop Data2-way ANOVA

Some of the hypotheses were supported.

There was a main effect forresidence. On-campusstudents earned higher GPAs (M=3.2545) than off-campus students (M=1.9667), F(1,14)=21.625,p

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Is there a sig. difference in funniness?Yet another excuse for a 1-way Anova

#1#2

#3

Rate each video on the following scale:

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Date post:	03-Apr-2018
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7___ANOVA 2-way

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